0
$\begingroup$

I have been trying to (rigorously) get the Minkowski's dimension (refer here for a basic definition) of the following:

$(x,y) : \{ y=x, x \in [-2, -1) \ \cup \ (1, 2]\} \ \ \cup \ \ \{ y=0, x \in [-1, 1] \} $.

$\endgroup$
1
$\begingroup$

If your boxes are size $k$, the first two segments can be covered in increments of $k\sqrt 2$ because they are along the diagonal of the square. The last segment is covered in increments of size $k$, so it takes $\frac 4k$ total boxes. The fact that the exponent on the $k$ is $-1$ says the dimension is $1$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.